Resonator



Dec. 27, 1949 A; E. BOWEN 2,492,680

RESONATOR Original Filed May 4, 1945 4 Sheets-Sheet 1 l i 377a,

1 v VENTOR AEBOWEN @TMWM A TTORNE Y Dec. 27, 1949 An E.IBCDVVEHQRESONATOR Original Filed May 4, 1943 4 Sheets-Sheet 2 FIG. 5

- //v l/EN TOR A. E. BOWEN Dec. 27, 1949 A, OWEN 2,492,680

RESONATOR Original Filed May 4, 1943 4 Sheets-Sheet 3 //vv/v TOR A. E.BOWEN ATTORNEY A. E. BOWEN Dec. 27, 1949 RESONATOR 4 Sheets-Sheet 4Original Filed May 4, 1943 FIG. I/

lNVE/VTOR A. E. BOWEN ATTORNEX Patented Dec. 27, 1949 UNITED STATESPATENT I RESONATOR.

mnolfla-S. 2Red Bank,.fN.-;i., astringent ancirazeienhnnemcratories,Incnrnoratedrhlew York N. Y., a corporationef New'dtotk Originalapplication Maya, r9 43, serlalflo." 1485.519. Divided and-thisapplication April 13,

1945, Serial No. 588,199.

claim. (01. Lit-44;). f

This invention relates to a resonator or resonating structureparticularly designed for microwaves, as tor *examplein the region of a10- centimeter wavelength, more or less.

a This application is (a aiivision-of-any copending application SerialNo. 485,579, filed May 4, 1943,

- and assigned to the sameassigneeas-the present particles such aselectrons, and electromagnetic waves guided orienclo'sedihyrelectricalconductors.

The invention will be described asa component partial 3Q gp'artoft-aihighgrreguencyielectronicsclevicegofthe qf .--.a vibra in 13, c lnn- Th type disclosed in the parenttapnlication.

In devices of this type, it is common practice :to" determinetheitraiectorieswithe charged particles either by means of an electricfield alone or.by a combination of-electric and magnetic fieldcomponents. Devices in which the combined type of trajectory control .isemployed Care tccmmonly rcalled ,magnetrons. {In cone almown.classoflmagnetrons.anelectriefield is maintained jlemimpressingapotential hetweenfiparallel 'p1ane plates ,v.while-. atathe same .time,aimagnetic field isL-m'aintai'ned parallel itovthe plates and hencep'erpendicular-itothe electric field. lit-is imown that electricallycharged particles upon being exposed to the action in. mutuallyperpendicular electric and magnetic fields and having initial velocitiesconfined to the direction perpendicular (to: both the electricandamagnetic field intensity vectors, move in cycloidal and trochoidalpaths. Inmagnetrons with cycloidal or trochoidal electron trajectories,use'has been made, as far as I am aware, only of that part of the energyresiding in the transverse component of the electron velocity. In otherwords, the energy utilized has been takeni'from "the electron 'duringthe :part of its 'motion p'erpendicular "to "the 1Dlanesbetween which it"moves.

- It is afeature of-the '-type of device IdlSCIOSGd in the arentapplication that energy is ab- :stracted from the electron when it istraveling parallel to the planes between which it moves. A device ofthis type may be embodied in an oscillator, an amplifiena repeater, andthe like, particularly for high frequency and micrmvaae applications,wherever generation, repetition, control orampliflcatienmfqelectromagnetic waves is an object. The '"resonator ofthe present invto In Canada April 12,

Mention anay 5116 .used .ith @the ideizicesdisclosed zin-fihe parentapplication izorein various other applications -.=for .ultrafi-hi hfrequencies 'gand imicrowanes. v

In :the aparticular .system-ciisclosedrherein and in themazrcntapplication,- a stream at char d particles is vconstrairieil tor-move i3raiec qry comprising a,iseriespf .cyclnidal ror, rtrochnida have.zmiqeressin ;.-a-1one ;-.a.;p ede erm n d alienationdscharact ri edahimth a ternate iintemz'als ;=e e1atwe1y hi h demand axia speed andaelativclyr v140w o ren wed j aisia sneed i11 other 1? :QYQLQEIQI .o.;;t q hci almotion mi er subst nt all 5Q 1Sfii i1 fier st Th d si rel tiely an 1 axial spee may con nien l nesi naredras ic ns. an the inte al39 :e1.a- Finely-low o rererse a i aim i s-gin c ar e 1 parti le shieQ1ie. to a F Y-QHQQ' A ui infla n JQH W b a fien a iq o a .:Qe. e t da i tdecele ated-.qe eetren 13mm density varied stream which may be usedtmeai- .cite ;oscil1ations in 1a resonator of .suitable iorm. The em d ee ia an o c tio exc t ien oper io arez arrie autat ioopsin th i le iegpath whilegthe :stream .,-is1density varied by withdrawing asome vofthe electrons drain the ;stream in .a tregion near a nodal point-pfthepath.

.Ithas already been proposed tp periorm upo n a stream of chargedparticles the operations-of velocity wariation, velocity :sort ing, tand-energy abstraction in that orderrindats ccessive points along I thepathiof the-.str.eam. It-i-is also knowr1 that 'velocityJwrtingnay be.efiected by curving or deflecting the stream. The arrange- ,mentsdisclosed hare an advantage not found in "prior devices, namely, thatthe path of the stream is kept away from the vicinity of the deflectingor controlling electrodes :except that those points where the operationsof velocity variation, removal of unwanted --.part'icles;and abstractionof energy are to be effected. As a result, energy lossesiand noisecnrigents caused -,by charged-particles striking -,-the deflecting, ,orcontrolling electrodestare largely avoided.

the ;dr.awing, .Eigwl .is a somewhat diagrammatical cross-emotional-vie.w --zof a ,typical mechanism pior.icontipllir g-v thetrajectorieslofea succession. -cf -.charged particles in -:ac.c01?.d%llwith the disclosure in the parent application;

Figs; 2, 3 and 4 are diaggams showing a variety o'f'proportionings, theessential parts of the trajectory control mechanism, includingresonators in -.accordance with the present invention;

Fig. 3 is a perspective view, partly broken away respect to plate 2.

l 3 showing an oscillator employing a resonator in accordance with theinvention;

Fig. 5-A is a plan View of the device of Fig. 5; Figs. 6 to 11,inclusive, are perspective views of various forms of resonators inaccordance with the invention. I r

The principles underlying the invention disclosed in the parentapplication are conveniently explained with reference to Fig. 1 whereinare represented diagrammatically two parallel plane plates l and 2separated a-distance a and maintained at a substantially constantpotential difference V0, plate I being positive with respect" to plate2. The resultant electric fieldintensity acts downward in the plane ofthe drawing as indicated by arrows in the figure. A cathode? is locatedin the plane of plate 2 and may be insulated from the plate so that thecathode may be a directly heated filament if desired. Slots or gaps 4and 5 are made'in plate I on centers spaced apart a distance 1rd, theslot 4 being located a horizontal distance /21ra from the cathode 3. Acollector plate 6 is located in the plane of plate" 2, insulatedtherefrom, and preferably maintained at a potential somewhat positivewith A substantially uniform magnetic field of intensity H is maintainedwith-its lines of force directed perpendicular to the plane of thedrawing in the sense away from the reader. It is assumed for the purposeof the explanation that the uniformity of the fields E and H is notmaterially disturbed by any edge efiects or by the presence of thecathode 3, the collector 6 or the slots 4 and '5. Assuming further thatelectrons are released with-zero velocity at the cathode 3, then,according to known principles the electrons will travel in trajectoriessuch as that shown in the curve -l,' which is a common cycloid. Theassumed conditions may readily be approximated in practice.

The equations of motion of an electron in the system of Fig. 1 arereadily set up and the equations of the electron paths under givenboundary conditions derived therefrom by conventional analyticalmethods. It is therefore deemed unnecessary to present a detailedsolution and only fth'e'basic equations and final results are set down Ilit mc d! where cis the velocity of light, and e, E, and H are to betaken as positive numbers. As the problem is fundamentally one of twodimensions only, itwill not be necessary to consider further they-coordinate nor Equation 2. Additional simplification of the analysismay be had by introducing the following abbreviations:

the use of which makes Theequations to be solved then reduce g al f' dtdz d z do; =P o'- The complete solution of the simultaneous Equations '7and 8 is from which the'following may be derived by diff erentiation forthe constants of'integration. I

From the general solutions (9) and 10) a particular solution may be hadfor thecase of particles starting from restat the origin at the timewhen t is zero by usinlg the initial conditions represented by i dt dt(15) to determine the constants of integration. The

result is readily found to be a: =%(pt sin pt) (16) the standardequations of a common cycloid.

Referring to the curve"! in Fig. l'the left-hand portion of the curverepresents the common cycloid of Equations 16 and 17. The curve willhave a maximum value of a for the condition I pt=1r (18) and at thispoint it will be found that I Assuming that the spacing a has been sochosen that the cycloidal trajectory Twill just graze the plate l,'i-twill be evident that the maximum z-coordinate of the trajectory will beequal to a and it will be found that at pt=1r,

mummies with the iinvention; a may variation is impressed upon theparticlescnsithey pass the first point of maximum z-coordinate, means ofa variable potential difierence across the slot 4 which will be suitablysuperposed the initial potential V *of "the plate -I as a whole. Thenthe potential'wliich acts upen'a given electron causing it to pass thegap 4 may expressed as V: V0+6 V0 where '16 is a small factor which [inordinaisy practice will-nsually lie within limits between eel and +1. Ifwe assume that a given electron leaves the gap 4 with a speed -sdetermined by theipotential V as given in p26) thenthe'equa tionrepresents the relationshiplbetween V and s based upon the conversion ofpotential energy into kinetic energy. I solvin'g (2-7) iars and using626-) gives VQ+6V0)6 T 't'flsing Vo=aE (29) together with and (.4), wehave s=2sm/m The trajectory of an electron after "it leaves the gap 4must' be suchasto' satisfythe eqnaticns of motion (1), (2) and (3) aswell as the new initial conditions ,produced by the velocity variation.The latter conditions are such that when P =1 (31) then 'a:=" '1ra ('32)m/ =1/ +a tea and da e Under these conditions it is readily fourid th'at-=%[pi (M 54) r l "(3a 02(11 -vm %[1' 2 /f1-+8 1=-) cos mt] (arEquations 36 and 3 7 willbe recognized as-the equations of 1a family oftrochoidsszgenerated by amovable:point,-distant,

from the center of a circle of di ametertdwvhich is rollin .upon andabove the line c t 1+ (as The .r-component of Velocity is -$=st1- mm -1-ws-p 1 (4 The 'trochoids corresponding irespectitrly to the values6=0.5,,- 6=0, and-6=+0.5 are plotted as curves' 8, $9 and i0. Curve 9 isa common cycloid, which is a special case of a trochoid.

Two important characteristics of the trajecmes to :he deduced from theabove analysis. mhe ifirst is that call the trajectories'a egarfilcss'iii tnezz-gap 't; 1 :The secondrlmportant aieii'uctfon ie that theaverage value of the -x=velocity et each particleiisiequal-tolso,independently ozf tliea va lue. In particular the resultis :found that the transit time'between itheigaps 4 and 5 the samefe'rall ithe iparticles regardless-of theleng'th and shape oftrajectory; 330th these-characteristics may be'verified by substituting31r in I (36) =-atid G8 wliich lgive's which expressions-are independentof 6' and det'ei iiime "the above-mentioned common point "at the gap t.-"I-he average speed of any particle while itrayersing the instancebetween the gaps fl' and ti is the int'er'gap distance ir'a div-idefl hythe transit time from 2ft"=irt0 nt-=31, which-speed amomits -to /1112),or So. I l hepassage of charged particles across gap j in adensi-tyvaried stream causes an alternating currentto'be"induced in the plate I.The stream is *g'iven a 'density-variation by the action (if theplate-Twhi'ch is so placed 'as to intercept particles 'ina group oftrajectories represented by curve "It: while particles *in a group of"trajectories represented by curve 8 pass on 'uninter cepted. "Thevelocity variation *impressed upon me 'stream at 'the gap 4' produces acyclical "variation in the trajectories 'o' f successive particlesranging in turn through trajectories of-the type of curve 8, thecycloidaltype 9, the type of curve It), the cycloidal type again andback to'the type of curve 8, etc. Only the particles followingtraj'e'ctories "ofthe'typ'et reachthe gap 5 and these form a densityvaried of intermittent stream at the gap 5. Plate 6 serves to "collectthe spent particles after they leave'the gap 5. The parts of thecurves*9 and I0 which'are unoccupied'by particles because of interception "byplate 2 ar shownfdotted in Fig. '1. j 'j It-wil-l'be" noted; that themechanism de'scr ea one "for "transforming a steady stream jffof chargedparticles into an intermittent -or density. varie'i'l stream. 'Itwilhbe'hotecliurther'ithat the grou ing of the particles is notdependent'up'or'i' the -=principle of fast moving particles overtak in'gslower moving particles. The principle" employed is one of segregating'th'ose'partioles which exceeda certain criticalvelooity. v H

It willbe noted "further that the charged pafrr; ticles approaching thegap 4'are' moving with'sfub stantially a uniform velocity and in a"'dirction parallel to the plate vI. This condition might lee-brought aboutin various Ways other than by locatingthe cathode 3 .in the plane ofstheplate 2 "and using the mechanism described foraproe 1 ducing thecycloidal trajectory I. For example,

the stream of chargedtparticles might be made to -approach the gap -4along a straight path parallel to the plate I under the influence of anelectric fie'ldin "the absence of the magnetic field H. The mechanismshown and the use oithfe cyldidahtra'jectory '1 will ordinarily besimplest and most expedient'but it wil-l'be understood that it is withinthe scope of the invention to eifipiey any suitable means to, provide astream of charged particles which approaches the gap 4 withsubstantially uniform velocity and charge density. I 1

In any case, after leaving the gap "4 the motion of the particles ischaracterized by a periodic the t-value pass through a common -poiiit uiear 13:5 component of motion in the direction of the electric fieldsuperposed upon a general proxression or drift in the directionperpendicular to theplane common to the electric and magnetic vectors.In the neighborhoods of ga 4 and gap the periodic component of motion inthe direction of the electric force produces a maximum displacement incompliance with the electric field. In the region where certain of thetrajectories meet the ground plate 2, the particles are movingg'inopposition to the electric field. In the casejof trajectories of thetype of curve It there is superposed upon the drift motion an incidentalperiodic component which could be utilized if circumstances warranted;

The velocity variation at the gap 4 effects a control over the periodicmotion in the direction of the electric force-,namely a control of theamplitude of such periodic motion. Under the variable amplitudecondition, however, all the variation is confined to the region in whichthe particles move against the force of the electric field, asdescribed, the excursion of the particles in compliance with theelectric force being limited to the uniform maximum value a by thecombined eil'ect of the electric and magnetic fields.

In the operation of the device as an amplifier, the potential of the gap4 is varied by means of the wave to be amplified and the outputresonator is connected across the gap 5. The spacing 1rd, between thegaps 4 and 5, as seen from (25), is a function of both E and H, varyindirectly as E and inversely as the square of H. The transit time betweenthe gaps is P and varies inversely with H, independently of E. There is,moreover, no critical transit time required in the amplifier case.

In the operation of-the device as an oscillator, the available values"of H are limited once the frequency of th desired oscillation isdetermined. It has been shown above that the particles which pass thegap 5 when the plate 2 is in place are those which are dcelerated at thegap 4. In

order for these particles to contribute energy to the field at the gap 5the particles must pass gap 5 while the field is opposing their motion.In a case where the gaps 4 and 5 are excited in such manner that thefields at the two gaps are poled in the same direction, an integralnumber of periods of the oscillation should elapse between the passageof a particle across the gap 4 and its subsequent passage across the gap5.

In terms of the frequency, f, the relation n 21' 2mm: 7 43) must hold,where n is any integer, or, in terms of the free space wavelength, x,

in which formula i is to be expressed in centimeters and H andwhichformula is applicable either to an amplifier or an oscillator.Since in the case of the electron oscillator )\H is given by (45), thespacing will be W a 2 m centimeters where V0 and are in electromagneticunits, A is in centimeters, and c=3 10 centimeter/seconds, or

centimeters (50) where A is in centimeters and V0 in volts.

A number of examples coming out of Formula 50 have been computed and areshown diagrammatically in Figs. 2, 3 and 4. It will be noted that forgiven values of 7x and V0, the spacing a is proportional to n. Thus if,as in Fig. 2, a has the value an corresponding to 11:1; then for thesame wavelength and same voltage, the spacing is 2ao for 11.:2, whichcase is shown in Fig. 3; and 3am for 12:3, as shown in Fig. 4. Thespacing of the gaps is equal to 1rd in every case. For a wavelength of10 centimeters and a voltage V0 of 1,000 volts, the value of ac comesout approximately 1 millimeter.

Various changes in the values of V0 and K may be made, at the same timechanging n so that the required spacing remains the same. For example,in Fig. 2 if n is made 2 and the wavelength and spacing remainunchanged, the voltage must be reduced to one-fourth its former value.The change in 11. also requires that H be reduced to one-half its formervalue, in order that (4'7) may be satisfied.

Several possible combinations of values for a 10 centimeter wavelengthin the diagram of Fig. 2 are tabulated in Table I.

2 Several possible combinations for a 10 centimeter wavelength in thediagram of Fig. 3 are given in Table II.

aneacso Combinations for the diagram of Fig. 4 are given in Table III.

Table III 41, cm. n V0, volts H, oersteds I, cm.

Conductors I4, I5 and I6 of a resonant circuit are shown schematically,connecting the plate segments I in Fig. 2. To indicate resonance at thesame wavelength in Figs. 3 and 4 as in Fig. 2, the areas enclosed by theconductors are shown approximately equal in all three figures.

Fig. 5 represents an embodiment of the invention in an oscillatorcomplete with a resonating circuit, an output coupling device and meansfor supplying the requisite electric and magnetic field intensities. Theequivalent of the plate I of Fig. 1 is represented in Fig. 5 by athreesegment anode having segments II, I2 and I3 connected together byconductors I4, I5 and I6, the latter, together with the anode segments,comprising a resonant circuit. The inductance of the resonant circuitresides mainly in the conductors I4, I5 and I6 while the capacitance ismainly between segments II and I2 at the gap 4 and between segments I2and I3 at the gap 5. The negative or ground plate 2 has a depression inwhich the cathode 3 is insulatingly mounted. These parts, together withthe collector plate 6,

are supported by rods held in a press I1 of conventional type formed inthe wall of a vacuumtight container I8, which wall may, for example, beof glass. The supporting rods may serve also as electrical connectionsfrom the plates to the sources of electromotive .force. The lattersources may constitute batteries or other suitable devices of which I9serves to heat the cathode, 20 to polarize the anode segments II, I2, I3positively with respect to the ground plate 2, and 2| serves to maintainthe collector 6 preferably at a somewhat positive potential with respectto the plate 2. Coupled to the conductors I4 and I6 is a coupling loop22 the ends of which may project through the envelope I8 and beconnected to any suitable load device for transmitting or utilizing thegenerated oscillations, the load circuit here being represented by aresistor 23. An electromagnet comprising pole-pieces 24, winding 25, ayoke 26 and energized by suitable means such as a battery 21, isprovided preferably external to the envelope I8 and is set up in such aposition (Fig. 5A) as to provide a magnetic field having lines of forcesubstantially parallel to the cathode 3 and the several plates.

The cycloidal path of a typical electron leaving the cathode 3 andapproaching the gap 4 is shown at 1. The path of this electron, shouldit be decelerated at the gap 4, is indicated at 8 showing that itstrajectory continues past the gap 5 and preferably. ends upon thecollector plate 6. Should. the same electron instead be accelerated atthe gap 4 its path is indicated at I0, ending upon the ground plate 2and not. reaching the p 5.

' The spacing between the ground plate and the anode is. determinedv as.described hereinbefore in connection with. Fig 1,. for a desiredoperating wavelength at a given voltage and for a chosen value of It,according. to The resonator is proportioned" to be resonant to theoperating wavelength. Furthendeta ilszofz the operation of the system ofFig. Swill be e ident from the explanation given hereinabove' inconnection with Fi 1. i

Fig. 6 shows a modification of the tuned circuit of Fig. 5. The anodesegments II and I3 of Fig. 5 are merged into a single segment I00 whichmay surround a middle segment IOI as shown. The inductive connectionbetween the segments I00 and I 0| comprises the conductors I4, I5 and I6corresponding to those similarly numbered in Fig. 5.

Fig. 7 shows a tuned circuit similar to that of Fig. 6 but with theinductive connection between the plates I00 and IOI simplified so as toeliminate the conductor I4.

Figs. 8 and 9 show tuned circuits similar in principle respectively tothe tuned circuits of Figs. 6 and 7.

In the arrangement of Fig. 8, a conductive bar I02 takes the place ofthe conductors I4, I5, I6, inclusive, of Fig. 6. In this kind ofstructure there is less inductance in the connector I02 and resonance isdetermined to a greater extent by distributed inductance in the segmentsI00 and IN.

In the arrangement of Fig. 9 the inductive connection I5, I6 is replacedby a bar I03. Here again the inductance relied upon for resonanceresides mainly in the distributed inductance of the segments I00 andIIII.

.Fig. 10 shows a tuned circuit comprising a pair of anode segments I04and I05 joined by an inductive conductor I06. The arrangement is mountedso that the plates I04 and I05 are coplanar with a guard plate I01 andare positioned in an opening therein. The conductor I06 is conductivelyconnected to and supported by a conductor I08 which is in turnconductively connected to and supported by the plate I01. The conductorI08, while it may represent an appreciable inductance can still serve asan untuned connection between the conductor I06 and the plate I01. It isonly necessary that the system I01, I08 shall not supportelectromagnetic oscillations at a frequency in the neighborhood of thedesired operating frequency. Under this condition, the anode segmentsI04 and I05 may sustain an alternating potential, while the plate I01and connector I08 will remain at a substantially unvarying potential.

Fig. 11 shows a tuned circuit which is a modification of that shown inFig. 10. A guard plate I01 has two openings within which the plates I04and I05 are positioned respectively. The conductor I06 connects theplates I04 and I05 as in Fig. 10 and a conductor I08 connects the middleof the conductor I06 to the portion of the plate I01 between the twoopenings.

What is claimed is:

A resonator comprising a conductive guard plate having a closed-slottherein, a pair of conductive plates mounted coplanarly with each otherand with said guard plate within the slot 11 in said uard plate, a firstinductive conductor connecting said pair. of conductive plates and lyingin a plane perpendicular to'the plane of said guard plate, and a secondinductive conductor lying in a plane perpendicular to the plane of saidguard plate, said second inductive conductor connecting said firstinductive conductor to said guard plate and thereby supporting said pairof conductive plates within the slot in said guard plate.

ARNOLD E. BOWEN.

REFERENCES CITED The following references are of record in the file ofthis patent:

12 UNITED STATES PATENTS Number Name Date Lindenblad May 26, 1936Hollmann Apr. 2, 1940 Mouromtseff et a1. Oct. 8, 1940 Fiske Sept. 3,1946 Fox Dec. 9, 1947 Dallenbach Mar. 9, 1948

